Mensa Spatial Reasoning 3 — Questions and Answers
Question 1: A cube is painted red on all faces and then cut into 27 equal smaller cubes. How many small cubes have exactly 2 red faces?
- 8
- 12 (Correct answer)
- 6
- 4
Correct answer: 12
The 12 edge cubes (not corners) each have exactly 2 painted faces.
Question 2: Which arrangement of 6 squares CANNOT be folded into a cube?
- A T-shaped arrangement
- A cross-shaped arrangement
- A straight 1×6 row (Correct answer)
- An L-shaped arrangement of 6 squares
Correct answer: A straight 1×6 row
A straight 1×6 row cannot fold into a cube because opposite faces would overlap.
Question 3: A shape is rotated 90° clockwise, then reflected across a vertical axis. Which single transformation produces the same result?
- 90° counter-clockwise rotation (Correct answer)
- 180° rotation
- Reflection across a horizontal axis
- Reflection across a diagonal axis
Correct answer: 90° counter-clockwise rotation
A 90° clockwise rotation followed by a vertical reflection is equivalent to a single 90° counter-clockwise rotation.
Question 4: Looking at a 4×4 grid from above, a ball starts at the top-left corner (row 1, col 1) and moves 2 squares right, then 3 squares down, then 1 square left. What is the ball's final position?
- Row 4, Column 2 (Correct answer)
- Row 3, Column 2
- Row 4, Column 3
- Row 3, Column 3
Correct answer: Row 4, Column 2
Starting at (row 1, col 1): right 2 → col 3; down 3 → row 4; left 1 → col 2, giving row 4, column 2.
Question 5: Which 3D shape produces an identical circular cross-section for every cut made parallel to its base?
- Sphere
- Cone
- Cylinder (Correct answer)
- Rectangular prism
Correct answer: Cylinder
A cylinder produces a circular cross-section for every cut parallel to its base.
Question 6: A rectangular piece of paper is folded in half along its length, then folded in half again along its width. A single hole is punched through all layers in the center. How many holes appear when the paper is fully unfolded?
- 1
- 2
- 4 (Correct answer)
- 8
Correct answer: 4
Each fold doubles the layers, so two folds create 4 layers, producing 4 holes when unfolded.
Question 7: Two identical right triangles are placed together along their hypotenuses. What shape is always formed?
- Rectangle
- Parallelogram (Correct answer)
- Rhombus
- Trapezoid
Correct answer: Parallelogram
Joining two identical right triangles along their hypotenuses always produces a parallelogram.
Mensa Spatial Reasoning 3
A cube is painted red on all faces and then cut into 27 equal smaller cubes.
How many small cubes have exactly 2 red faces?